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A287650 Number of double symmetric diagonal Latin squares of order 2n with constant first string. 1
0, 2, 0, 15780 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Double symmetric square has symmetries both in horizontal and vertical planes.

LINKS

Table of n, a(n) for n=1..4.

E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian)

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, Estimating of combinatorial characteristics for diagonal Latin squares, Recognition — 2017 (2017), pp. 98-100 (in Russian)

EXAMPLE

Double symmetric diagonal Latin square example:

0 1 2 3 4 5 6 7

6 2 3 7 0 4 5 1

4 5 1 0 7 6 2 3

5 6 7 4 3 0 1 2

7 3 6 2 5 1 4 0

2 7 4 1 6 3 0 5

3 0 5 6 1 2 7 4

1 4 0 5 2 7 3 6

In horizontal plane present a one-to-one correspondence between elements 0 and 7, 1 and 6, 2 and 5, 3 and 4. In vertical plane also present a correspondence between elements 0 and 1, 1 and 4, 2 and 0, 3 and 5, etc.

CROSSREFS

Cf. A003191, A287649.

Sequence in context: A265594 A269904 A090446 * A270830 A270829 A104157

Adjacent sequences:  A287647 A287648 A287649 * A287651 A287652 A287653

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, May 29 2017

STATUS

approved

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Last modified August 19 08:57 EDT 2017. Contains 290794 sequences.